Fantasy: LOTR trilogy
Drama: A Few Good Men
Comedy: Twilight
Anime: Spirited Away
Sci Fi: any even numbered Star Trek
Horror: the original Carrie
Hard to Classify: The Truman Show (sci fi/comedy/drama/prophetic?? ;)
Action: The Running Man (I'd like to see Ben Richards vs Katniss, haha!)
Romance: The Princess Bride

Hm, I don't think I'm qualified to answer: all the movies I've ever seen fit into the same genre - FMV adventures.

Sci-Fi: 2001

Crime: Sleth

Thriller: Jacob's Ladder

Historical War: Paths of Glory

Modern-ish War: Platoon

Drama: Gangs of New York

Superhero: Batman 2 (with Penguin)

Horror: Exorcist

Musical: Fiddler on the Roof

Animated: Akira

Comady: Joe Vs the Volcano

Acttion/adventure: Indiana Jones and the Temple of Doom

I tried to pick only the film I feel really best about. I do think these are all very good, but to get into film theory and criticism would complicate and change my answers. These are my favorites in the sense of I love them and feel very good watching them again.

Sci Fi: 12 Monkeys

Historical: The Return of Martin Guerre

Historical Fiction: The Last Valley

Comedy: Hot Fuzz

Crime: Rashomon

Action: Leon The Professional

Fantasy: WILLOW !!!

Anime: Tekkonkinkreet

Slice of Life: Magnolia

War: Das Boot

Have you ever heard of a little-known gem of a movie called "Zardoz?" Judging by your picks, I think there's a good chance you might like it!

Hope you don't mind I steal your format, Elmofongo :)

Sci-Fi: Star Wars Series

Crime: Scarface

Thriller: Silence of the Lambs/ Sixth Sense

Historical War: Band of Brothers (Miniseries)

Modern-ish War: Black Hawk Down

Drama: Shawshank Redemption/Schindler's List

Superhero: The Dark Knight

Horror: Alien

Musical: Westside Story/South Pacific

Animated: Toy Story

Comedy: Step Brothers

Acttion/adventure: Django Unchained

That movie is epic!